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Short descriptionQuantitative methods enable people to make good decisions and to organize and understand numbers. This book acts as a gentle introduction to quantitative methods for the conscious manager, emphasizing not only the role of data in making better decisions, but also the pitfalls of relying too heavily on software packages to implement standard statistical procedures. Divided into four parts, the book covers motivations and foundations; elementary probability and statistics; decision making models; and advanced statistical modeling. It is ideal as a reference and self-study for financial and business economic professionals, as well as a graduate-level textbook.

From the contentsPreface.

Part I. Motivations and Foundations.

1 Quantitative Methods: Should we Bother?.

1.1 A decision problem without uncertainty: product mix.

1.2 The role of uncertainty.

1.3 Endogenous vs. exogenous uncertainty: Are we alone?.

1.4 Quantitative models and methods.

1.5 Quantitative analysis and problem solving.

Problems.

For further reading.

References.

2 Calculus.

2.1 A motivating example: economic order quantity.

2.2 A little background.

2.3 Functions.

2.4 Continuous functions.

2.5 Composite functions.

2.6 Inverse functions.

2.7 Derivatives.

2.8 Rules for calculating derivatives.

2.9 Using derivatives for graphing functions.

2.10 Higher-order derivatives and Taylor expansions.

2.11 Convexity and optimization.

2.12 Sequences and series.

Problems.

For further reading.

References.

3 Linear Algebra.

3.1 A motivating example: binomial option pricing.

3.2 Solving systems of linear equations.

3.3 Vector algebra.

3.4 Matrix algebra.

3.5 Linear spaces.

3.6 Determinant.

3.7 Eigenvalues and eigenvectors.

3.8 Quadratic forms.

3.9 Calculus in multiple dimensions.

Problems.

For further reading.

References.

Part II Elementary Probability and Statistics.

4 Descriptive Statistics: On the Way to Elementary Probability.

4.1 What is Statistics?.

4.2 Organizing and representing raw data.

4.3 Summary measures.

4.4 Cumulative frequencies and percentiles.

4.5 Multidimensional data.

Problems.

For further reading.

References.

5 Probability Theories.

5.1 Different concepts of probability.

5.2 The axiomatic approach.

5.3 Conditional probability and independence.

5.4 Total probability and Bayes' theorems.

Problems.

For further reading.

References.

6 Discrete Random Variables.

6.1 Random variables.

6.2 Characterizing discrete distributions.

6.3 Expected value.

6.4 Variance and standard deviation.

Problems.

For further reading.

References.

7 Continuous Random Variables.

7.1 Building intuition: from discrete to continuous random variables.

7.2 Cumulative distribution and probability density functions.

7.3 Expected value and variance.

7.4 Mode, median, and quantiles.

7.5 Higher-order moments, skewness, and kurtosis.

7.6 A few useful continuous probability distributions.

7.7 Sums of independent random variables.

7.8 Miscellaneous applications.

7.9 Stochastic processes.

7.10 Probability spaces, measurability, and information.

Problems.

For further reading.

References.

8 Dependence, Correlation, and Conditional Expectation.

8.1 Joint and marginal distributions.

8.2 Independent random variables.

8.3 Covariance and correlation.

8.4 Jointly normal variables.

8.5 Conditional expectation.

Problems.

For further reading.

References.

9 Inferential Statistics.

9.1 Random samples and sample statistics.

9.2 Confidence intervals.

9.3 Hypothesis testing.

9.4 Beyond the mean of one population.

9.5 Checking the fit of hypothetical distributions: the chi-square test.